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Related Concept Videos

Active Filters01:25

Active Filters

Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:
Passive Filters01:27

Passive Filters

Passive filters are utilized to shape the frequency spectrum of signals across a diverse array of applications. These filters, using only passive elements like resistors (R), inductors (L), and capacitors (C), are capable of selectively allowing or blocking certain frequency ranges without the need for external power sources.
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff frequency...
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
State Space to Transfer Function01:21

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
Transfer Function to State Space01:23

Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
Second-order Op Amp Circuits01:19

Second-order Op Amp Circuits

Implementing second-order low-pass filters in audio systems is crucial in refining audio signals by eliminating undesirable high-frequency noise. These filters typically involve second-order op-amp circuits configured as voltage followers, encompassing two nodes with distinct storage elements.
The analysis of such circuits follows a systematic approach, similar to the second-order RLC circuits. In practical scenarios, bulky inductors are rarely employed due to their size and weight. This means...

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Factorizable state-space model for active optical filter structures with two-port couplers.

Issa Panahi1, Govind Kannan

  • 1Statistical Signal Processing Laboratory, Department of Electrical Engineering, University of Texas at Dallas, 800 West Campbell Road, Richardson, Texas 75080, USA.

Applied Optics
|June 12, 2008
PubMed
Summary
This summary is machine-generated.

A new state-space model (SSM) analyzes integrated photonic lattice filters. This model separates fixed coupler structures from tunable semiconductor optical amplifier gains, enabling efficient analysis and loss compensation.

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Area of Science:

  • Integrated photonics
  • Optical filter design
  • Semiconductor device physics

Background:

  • Integrated photonic architectures offer miniaturization and enhanced functionality.
  • Lattice filter structures are crucial for optical signal processing.
  • Controlling optical gain and loss is essential for device performance.

Purpose of the Study:

  • To develop a state-space model (SSM) for a novel integrated photonic lattice filter architecture.
  • To provide a systematic analysis framework for devices combining couplers and semiconductor optical amplifiers (gains).
  • To explore the use of tunable gains for both gain control and loss compensation.

Main Methods:

  • Development of a state-space model (SSM) for the integrated photonic architecture.
  • Factorization of the SSM into matrices representing structural parameters and tunable gains.
  • Extension of the model to multiple-input, multiple-output (MIMO) filter structures.

Main Results:

  • The SSM is successfully factorized, separating static coupler properties from dynamic gain elements.
  • The model facilitates a practical analysis of the lattice filter structure.
  • A novel method for utilizing semiconductor optical amplifier gains as loss compensation elements was demonstrated.

Conclusions:

  • The developed state-space model offers a systematic approach to analyzing integrated photonic lattice filters.
  • The model's factorization simplifies analysis and allows for extension to complex filter designs.
  • The dual role of semiconductor optical amplifiers as tunable elements and loss compensators is a significant advancement.